Axisymmetric dynamic stability of an annular plate subject to pulsating conservative radial loads

Abstract

The equations of motion of an annular plate subject to prescribed timedependent radial compressive loads are formulated based on Hamilton's principle and the assumed mode method. The effects of sinusoidal perturbations in respect of the radial loads are then examined using Bolotin's method. The respective regions of instability for axisymmetric deformations are determined by converting the resulting equations of motion to the standard form of a generalized eigenvalue problem. Instability regions are presented for various combinations of average value and amplitude of the sinusoidal perturbations of the radial loads and also for various edge conditions for an isotropic annular plate. The unstable regions are found to be insensitive to changes in the average in-plane load when the annular plate is loaded only on the inner edge. The unstable regions for the case where the plate is loaded on both edges are similar to the case where the plate is loaded only on the outer edge.